Finite element modeling of dual convection in a Y shaped porous cavity containing viscus fluid

Abstract

This communication analyzes the dual convection regime of Newtonian fluid flow in a Y shaped porous enclosure with heat and mass distribution, using a mathematical model of dimensionless PDEs and an effective finite element method. The top curved wall of the enclosure is assumed hot and side walls are cold while the bottom wall is assumed adiabatic. The problem is discretized using P2 and P1 finite element methods to approximate the displacement, pressure, and velocity. The linearized system of equations is solved using Newton’s iterative scheme. The study evaluates the impact of key parameters such as the Hartmann number, Lewis number, Rayleigh number, and buoyancy ratio on the flow, heat transfer rate, and mass transfer rate. Results indicate that an increase in the Hartmann number, Rayleigh numbers and buoyancy ratio amplifies both mass and heat transfer rates. The buoyancy ratio has a noteworthy impact on the flow and transfer rates, with a greater influence seen for. The study presents graphical representations of flow and temperature fields, as well as Nusselt and Sherwood numbers provide a comprehensive visualization of the results. Heat and mass transfer rate is minimum for concentration dominated counter flow (N=−2) and maximum for concentration dominated assisting flow N=2.

Heat Transfer Investigation in Plus-Shaped Enclosure Using Power Law Fluid: A Finite Element Approach

“…This method generates a series of functions within subdomains intended for approximation within Sobolev test spaces, providing a measure of function smoothness and suitability for solving partial differential equation (PDE) problems. The weak formulation of flows of Bingham-type fluids is discussed in [42], while [43] focuses on laminar, uniform, and incompressible flow, and [40] addresses the power law fluid model. The given expression represents the weak form of Equations ( 7)- (11), as described in [38,40].…”